polynomials_p.cc

// ---------------------------------------------------------------------
//
// Copyright (C) 2004 - 2018 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE.md at
// the top level directory of deal.II.
//
// ---------------------------------------------------------------------


#include <deal.II/base/polynomials_p.h>

DEAL_II_NAMESPACE_OPEN


template <int dim>
PolynomialsP<dim>::PolynomialsP(const unsigned int p)
  : PolynomialSpace<dim>(
      Polynomials::Monomial<double>::generate_complete_basis(p))
  , p(p)
{
  std::vector<unsigned int> index_map(this->n());
  create_polynomial_ordering(index_map);
  this->set_numbering(index_map);
}


template <>
void
PolynomialsP<1>::create_polynomial_ordering(
  std::vector<unsigned int> &index_map) const
{
  Assert(index_map.size() == this->n(),
         ExcDimensionMismatch(index_map.size(), this->n()));

  // identity
  for (unsigned int i = 0; i < this->n(); ++i)
    index_map[i] = i;
}


namespace
{
  const unsigned int imap2[6][21] = {
    {0},
    {0, 1, 2},
    {0, 1, 3, 4, 2, 5},
    {0, 1, 4, 5, 2, 7, 6, 8, 3, 9},
    {0, 1, 5, 6, 2, 9, 7, 10, 3, 12, 11, 8, 13, 4, 14},
    {0, 1, 6, 7, 2, 11, 8, 12, 3, 15, 13, 9, 16, 4, 18, 14, 17, 10, 19, 5, 20}};
}

template <>
void
PolynomialsP<2>::create_polynomial_ordering(
  std::vector<unsigned int> &index_map) const
{
  Assert(index_map.size() == this->n(),
         ExcDimensionMismatch(index_map.size(), this->n()));
  Assert(p <= 5, ExcNotImplemented());

  // Given the number i of the
  // polynomial in
  // @f$1,x,y,xy,x2,y2,...@f$,
  // index_map[i] gives the number of
  // the polynomial in
  // PolynomialSpace.
  for (unsigned int i = 0; i < this->n(); ++i)
    index_map[i] = imap2[p][i];
}


namespace
{
  const unsigned int imap3[4][20] = {{0},
                                     {0, 1, 2, 3},
                                     {0, 1, 3, 6, 4, 7, 8, 2, 5, 9},
                                     {0,  1, 4,  10, 5,  11, 13, 2, 7, 16,
                                      14, 6, 12, 8,  15, 17, 18, 3, 9, 19}};
}

template <>
void
PolynomialsP<3>::create_polynomial_ordering(
  std::vector<unsigned int> &index_map) const
{
  Assert(index_map.size() == this->n(),
         ExcDimensionMismatch(index_map.size(), this->n()));
  Assert(p <= 3, ExcNotImplemented());

  // Given the number i of the
  // polynomial in
  // @f$1,x,y,xy,x2,y2,...@f$,
  // index_map[i] gives the number of
  // the polynomial in
  // PolynomialSpace.
  for (unsigned int i = 0; i < this->n(); ++i)
    index_map[i] = imap3[p][i];
}



template class PolynomialsP<1>;
template class PolynomialsP<2>;
template class PolynomialsP<3>;

DEAL_II_NAMESPACE_CLOSE